mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-28 23:22:54 +00:00
Jukka Aho
347 lines
13 KiB
Julia
347 lines
13 KiB
Julia
# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
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using JuliaFEM
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using JuliaFEM.Test
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using JuliaFEM.Preprocess
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using JuliaFEM.Postprocess
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@testset "Tet10 + convection" begin
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# For some reason Tet10 fails, maybe because of convection.
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mesh_file = Pkg.dir("JuliaFEM") * "/test/testdata/primitives.med"
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mesh = aster_read_mesh(mesh_file, "Tet10")
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prob = Problem(Heat, "tet", 1)
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face = Problem(Heat, "face 4", 1)
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fixed = Problem(Dirichlet, "fixed face 3", 1, "temperature")
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prob.elements = create_elements(mesh, "TET")
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update!(prob, "temperature thermal conductivity", 50.0)
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face.elements = create_elements(mesh, "FACE4")
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update!(face, "temperature external temperature", 20.0)
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update!(face, "temperature heat transfer coefficient", 60.0)
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fixed.elements = create_elements(mesh, "FACE2")
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info("# of elements in fixed set: $(length(fixed))")
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update!(fixed, "temperature 1", 0.0)
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solver = LinearSolver(prob, face, fixed)
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call(solver)
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T = prob.assembly.u
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info("Solution: $T")
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T_expected = [ # using code aster
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1.45606533688540E+01
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5.01315339269860E-17
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3.02236827927507E-17
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-2.01049663215778E-16
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1.05228712963739E+01
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0.00000000000000E+00
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9.44202309239159E+00
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1.05228712963739E+01
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4.44089209850063E-16
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0.00000000000000E+00]
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@test isapprox(T, T_expected; rtol=1.0e-6)
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end
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@testset "one element heat problem" begin
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X = Dict{Int, Vector{Float64}}(
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1 => [0.0,0.0],
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2 => [1.0,0.0],
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3 => [1.0,1.0],
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4 => [0.0,1.0])
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# define volume element
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el1 = Element(Quad4, [1, 2, 3, 4])
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update!(el1, "geometry", X)
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update!(el1, "temperature thermal conductivity", 6.0)
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update!(el1, "temperature load", 12.0)
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# define boundary element for flux
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el2 = Element(Seg2, [1, 2])
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update!(el2, "geometry", X)
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# linear ramp from 0 -> 6 in time 0 -> 1
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update!(el2, "temperature flux", 0.0 => 0.0, 1.0 => 6.0)
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# define heat problem and push elements to problem
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problem = Problem(Heat, "one element heat problem", 1)
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problem.properties.formulation = "2D"
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push!(problem, el1, el2)
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# define boundary element for dirichlet boundary condition
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el3 = Element(Seg2, [3, 4])
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update!(el3, "geometry", X)
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update!(el3, "temperature 1", 0.0)
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boundary_condition = Problem(Dirichlet, "T=0 on top", 1, "temperature")
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push!(boundary_condition, el3)
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# manual assembling of problem + solution:
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assemble!(problem, 0.0)
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A = full(problem.assembly.K)
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b = full(problem.assembly.f)
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A_expected = [
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4.0 -1.0 -2.0 -1.0
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-1.0 4.0 -1.0 -2.0
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-2.0 -1.0 4.0 -1.0
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-1.0 -2.0 -1.0 4.0]
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free_dofs = [1, 2]
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@test isapprox(A, A_expected)
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@test isapprox(A[free_dofs, free_dofs] \ b[free_dofs], [1.0, 1.0])
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# using Solver
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solver = LinearSolver("solve heat problem")
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push!(solver, problem, boundary_condition)
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# Set constant source f=12 with k=6. Accurate solution is
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# T=1 on free boundary, u(x,y) = -1/6*(1/2*f*x^2 - f*x)
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# when boundary flux not active (at t=0)
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solver.time = 0.0
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call(solver)
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# interpolate temperature at middle of element 2 (flux boundary) at time t=0:
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T = el2("temperature", [0.0], 0.0)
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@test isapprox(T[1], 1.0)
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# Set constant flux g=6 on boundary. Accurate solution is
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# u(x,y) = x which equals T=1 on boundary.
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# at time t=1.0 all loads should be on.
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solver.time = 1.0
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call(solver)
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T = el2("temperature", [0.0], 1.0)
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@test isapprox(T[1], 2.0)
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end
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function T_acc(x)
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# accurate solution
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a = 0.01
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L = 0.20
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k = 50.0
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Tᵤ = 20.0
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h = 10.0
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P = 4*a
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A = a^2
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α = h
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β = sqrt((h*P)/(k*A))
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T̂ = 100.0
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C = [1.0 1.0; (α+k*β)*exp(β*L) (α-k*β)*exp(-β*L)] \ [T̂-Tᵤ, 0.0]
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return dot(C, [exp(β*x), exp(-β*x)]) + Tᵤ
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end
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#=
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@testset "test 1d heat problem" begin
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X = Dict{Int, Vector{Float64}}(
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1 => [0.0, 0.0, 0.0],
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2 => [0.1, 0.0, 0.0],
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3 => [0.2, 0.0, 0.0])
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e1 = Element(Seg2, [1, 2])
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e2 = Element(Seg2, [2, 3])
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e3 = Element(Poi1, [3])
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p1 = Problem(Heat, "1d heat problem", 1)
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p1.properties.formulation = "1D"
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push!(p1, e1, e2, e3)
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update!(p1, "geometry", X)
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a = 0.010
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update!(p1, "cross-section area", a^2)
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update!(p1, "cross-section perimeter", 4*a)
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update!(p1, "temperature thermal conductivity", 50.0) # k [W/(m∘C)]
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update!(p1, "temperature heat transfer coefficient", 10.0) # h [W/(m²∘C)]
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update!(p1, "temperature external temperature", 20.0)
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p2 = Problem(Dirichlet, "left boundary", 1, "temperature")
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e3 = Element(Poi1, [1])
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update!(e3, "geometry", X)
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update!(e3, "temperature 1", 100.0)
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push!(p2, e3)
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solver = LinearSolver(p1, p2)
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call(solver)
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T_min = minimum(p1.assembly.u)
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@test isapprox(T_max, T_acc(0.2); rtol=4.5e-2)
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end
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=#
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@testset "compare simple 3d heat problem to code aster solution" begin
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fn = Pkg.dir("JuliaFEM") * "/test/testdata/rod_short.med"
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mesh = aster_read_mesh(fn, "Hex8")
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element_sets = join(keys(mesh.element_sets), ", ")
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info("element sets: $element_sets")
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p1 = Problem(Heat, "rod", 1)
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rod = create_elements(mesh, "ROD")
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face2 = create_elements(mesh, "FACE2")
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face3 = create_elements(mesh, "FACE3")
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face4 = create_elements(mesh, "FACE4")
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face5 = create_elements(mesh, "FACE5")
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face6 = create_elements(mesh, "FACE6")
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update!(rod, "temperature thermal conductivity", 50.0)
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update!(face2, "temperature external temperature", 20.0)
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update!(face2, "temperature heat transfer coefficient", 60.0)
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update!(face3, "temperature external temperature", 30.0)
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update!(face3, "temperature heat transfer coefficient", 50.0)
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update!(face4, "temperature external temperature", 40.0)
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update!(face4, "temperature heat transfer coefficient", 40.0)
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update!(face5, "temperature external temperature", 50.0)
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update!(face5, "temperature heat transfer coefficient", 30.0)
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update!(face6, "temperature external temperature", 60.0)
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update!(face6, "temperature heat transfer coefficient", 20.0)
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push!(p1, rod, face2, face3, face4, face5, face6)
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p2 = Problem(Dirichlet, "left support T=100", 1, "temperature")
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push!(p2, create_elements(mesh, "FACE1"))
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update!(p2, "temperature 1", 100.0)
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solver = LinearSolver(p1, p2)
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call(solver)
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# fields extracted from Code Aster .resu file
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TEMP = Dict{Int64, Float64}(
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1 => 1.00000000000000E+02,
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2 => 1.00000000000000E+02,
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3 => 1.00000000000000E+02,
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4 => 1.00000000000000E+02,
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5 => 3.01613322896279E+01,
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6 => 3.01263406641066E+01,
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7 => 3.02559777927923E+01,
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8 => 3.02209215997131E+01)
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FLUX_ELGA = Dict{Int64, Vector{Float64}}(
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1 => [1.74565160615448E+04, -9.99903237329079E+01, -3.69874201221677E+01],
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2 => [1.74565160615448E+04, -3.73168968436642E+02, -1.38038931136833E+02],
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3 => [1.74428571293096E+04, -9.99903237329079E+01, -3.70268090662933E+01],
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4 => [1.74428571293096E+04, -3.73168968436642E+02, -1.38185932677561E+02],
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5 => [1.74615686370955E+04, -9.99509347888079E+01, -3.69874201221677E+01],
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6 => [1.74615686370955E+04, -3.73021966895897E+02, -1.38038931136833E+02],
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7 => [1.74479150854902E+04, -9.99509347888065E+01, -3.70268090662933E+01],
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8 => [1.74479150854901E+04, -3.73021966895874E+02, -1.38185932677561E+02])
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FLUX_NOEU = Dict{Int64, Vector{Float64}}(
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1 => [1.74596669275930E+04, 7.55555618070503E-11, 3.68594044175552E-12],
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2 => [1.74684148339734E+04, 1.10418341137120E-11, 3.48876483258209E-12],
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3 => [1.74360055518019E+04, 7.91828824731056E-11, 1.95399252334028E-13],
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4 => [1.74447696000717E+04, -3.49587025993969E-12, 3.55271367880050E-13],
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5 => [1.74596669275931E+04, -4.73227515822099E+02, -1.74958127606525E+02],
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6 => [1.74684148339733E+04, -4.72904678032251E+02, -1.74958127606524E+02],
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7 => [1.74360055518019E+04, -4.73227515822118E+02, -1.75280965396335E+02],
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8 => [1.74447696000717E+04, -4.72904678032179E+02, -1.75280965396335E+02])
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postprocessor = Postprocessor(p1)
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flux = full(call(postprocessor))
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fluxd = Dict{Int64, Vector{Float64}}()
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for j=1:8
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fluxd[j] = vec(flux[j,:])
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end
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T = p1("temperature")
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for j in sort(collect(keys(T)))
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T1 = T[j][1]
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T2 = TEMP[j]
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rtol = norm(T1-T2)/max(T1,T2)*100.0
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@printf "node %i temp, JF: %e, CA: %e, rtol: %10.6f %%\n" j T1 T2 rtol
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@test rtol < 1.0e-9
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end
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for j=1:8
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q1 = get_integration_points(first(rod))[j]("heat flux", 0.0)
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q2 = FLUX_ELGA[j]
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rtol = norm(q1-q2)/max(norm(q1),norm(q2))*100.0
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@printf "ip %i flux, JF: (% e,% e,% e), CA: (% e,% e,% e), rtol: %10.6f %%\n" j q1... q2... rtol
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# @test rtol < 0.05
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# testing in integration points makes no sense because they are in different order in CA
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end
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for j in sort(collect(keys(fluxd)))
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q1 = fluxd[j]
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q2 = FLUX_NOEU[j]
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rtol = norm(q1-q2)/max(norm(q1),norm(q2))*100.0
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@printf "node %i flux, JF: (% e,% e,% e), CA: (% e,% e,% e), rtol: %10.6f %%\n" j q1... q2... rtol
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@test rtol < 1.0e-9
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end
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end
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@testset "compare simple 3d heat problem to analytical solution" begin
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function calc_3d_heat_model(mesh_name)
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fn = Pkg.dir("JuliaFEM") * "/test/testdata/rod_short.med"
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mesh = aster_read_mesh(fn, mesh_name)
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p1 = Problem(Heat, "rod", 1)
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p2 = Problem(Dirichlet, "left support T=100", 1, "temperature")
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p1.elements = create_elements(mesh, "ROD", "FACE2")
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p2.elements = create_elements(mesh, "FACE1")
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update!(p1, "temperature thermal conductivity", 100.0)
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update!(p1, "temperature external temperature", 0.0)
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update!(p1, "temperature heat transfer coefficient", 1000.0)
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update!(p2, "temperature 1", 100.0)
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solver = LinearSolver(p1, p2)
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call(solver)
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T_min = minimum(p1.assembly.u)
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return T_min
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end
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for model in ["Tet4", "Tet10", "Hex8", "Hex20", "Hex27"]
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Tmin = calc_3d_heat_model(model)
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Tacc = 100/3
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rtol = norm(Tmin-Tacc)/max(Tmin,Tacc)*100.0
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@printf "%-10s : Tmin = % g, Tacc = % g, rtol = %g %%\n" model Tmin Tacc rtol
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@test isapprox(Tmin, 100/3)
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end
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end
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@testset "compare simple 3d heat problem to code aster solution" begin
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function calc_3d_heat_model(mesh_name)
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fn = Pkg.dir("JuliaFEM") * "/test/testdata/rod_short.med"
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mesh = aster_read_mesh(fn, mesh_name)
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element_sets = join(keys(mesh.element_sets), ", ")
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info("element sets: $element_sets")
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# x -> FACE1 ... FACE2
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# y -> FACE3 ... FACE4
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# z -> FACE5 ... FACE6
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# rod has longer dimension in x direction, first face comes
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# first in corresponding axis direction
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p1 = Problem(Heat, "rod", 1)
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rod = create_elements(mesh, "ROD")
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face2 = create_elements(mesh, "FACE2")
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face3 = create_elements(mesh, "FACE3")
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face4 = create_elements(mesh, "FACE4")
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face5 = create_elements(mesh, "FACE5")
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face6 = create_elements(mesh, "FACE6")
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update!(rod, "temperature thermal conductivity", 50.0)
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update!(face2, "temperature external temperature", 20.0)
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update!(face2, "temperature heat transfer coefficient", 60.0)
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update!(face3, "temperature external temperature", 30.0)
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update!(face3, "temperature heat transfer coefficient", 50.0)
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update!(face4, "temperature external temperature", 40.0)
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update!(face4, "temperature heat transfer coefficient", 40.0)
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update!(face5, "temperature external temperature", 50.0)
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update!(face5, "temperature heat transfer coefficient", 30.0)
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update!(face6, "temperature external temperature", 60.0)
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update!(face6, "temperature heat transfer coefficient", 20.0)
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push!(p1, rod, face2, face3, face4, face5, face6)
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p2 = Problem(Dirichlet, "left support T=100", 1, "temperature")
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p2.elements = create_elements(mesh, "FACE1")
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update!(p2, "temperature 1", 100.0)
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solver = LinearSolver(p1, p2)
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call(solver)
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return p1.assembly.u
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end
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CA_sol = Dict(
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"Tet4" => 3.01872246268290E+01,
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"Hex8" => 3.01263406641066E+01,
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"Tet10" => 4.38924023356612E+01,
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"Hex20" => 4.57539800177123E+01,
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"Hex27" => 4.57760386068096E+01)
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models = ["Tet4", "Hex8", "Hex20", "Hex27", "Tet10"]
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for model in models
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T = calc_3d_heat_model(model)
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T_min = minimum(T)
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T_ca = CA_sol[model]
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rtol = norm(T_min-T_ca)/max(T_min,T_ca)*100.0
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@printf "%-10s : T_min = % g, T_ca = % g, rtol = %g %%\n" model T_min T_ca rtol
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if rtol > 1.0e-9
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info("Solution vector")
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dump(T)
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end
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@test rtol < 1.0e-9
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end
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end
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